Hypermatrix factors for string and membrane junctions

Yuhan Fang, Shir Levkowitz, Hisham Sati, Daniel Thompson

Research output: Contribution to journalArticlepeer-review


The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n) and Sp(n) are, respectively, tensor, antisymmetric and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provides such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of 3-junctions of strings and membranes. Generalizations are also considered.

Original languageEnglish (US)
Article number505401
JournalJournal of Physics A: Mathematical and Theoretical
Issue number50
StatePublished - Dec 17 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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